Before the Matan Torah, did HaShem issue divorce regulations?

Question

I am an Italian son of Noah.

The Torah (written and especially oral) establishes a detailed regulation of the divorce institute. According to Jewish tradition, before the giving of the Torah were there prescriptions on the matter given by the Creator? I do not know if the episode of Abraham who sends Hagar away can provide precise information in this sense, as it is true that in Genesis 16:3 it is written:

וַתִּקַּ֞ח שָׂרַ֣י אֵֽשֶׁת־אַבְרָ֗ם אֶת־הָגָ֤ר הַמִּצְרִית֙ שִׁפְחָתָ֔הּ מִקֵּץ֙ עֶ֣שֶׂר שָׁנִ֔ים לְשֶׁ֥בֶת אַבְרָ֖ם בְּאֶ֣רֶץ כְּנָ֑עַן וַתִּתֵּ֥ן אֹתָ֛הּ לְאַבְרָ֥ם אִישָׁ֖הּ ל֥וֹ לְאִשָּֽׁה׃

"So Sarai, Abram's wife, took Hagar the Egyptian, her handmaid, at the end of ten years of Abram's dwelling in the land of Canaan, and she gave her to Abram her husband for a wife."

But in Genesis 21:12–13, HaShem addresses Abraham by calling Hagar simply "your handmaid", and not "your wife". I do not understand therefore if in this case there has been a real divorce.

Answer 1

The Maggid Mishne (Rav Vidal of Tolosa, spain 14th century) on the Rambam Hilchot Ishut 1,1 says that before Mattan Torah (giving the Torah to Israel) everyone had a status of a gentile and he cross-references to Hilchot Melachim 9 for all the rules of marriage:

קודם מתן תורה היה אדם פוגע אשה בשוק אם רצה הוא והיא לישא אותה מכניסה לתוך בית - ובועלה בינו לבין עצמו ותהיה לו לאשה וזה פשוט ומבואר בהרבה מקומות דלנכרי בייחוד בעלמא הויא אשתו וכנזכר פרק ט' מהלכות מלכים

Before the Torah was given, a man met a woman, she would enter his domain with consent as a designated wife, consummate privately and they would be married since a Gentile (Jews were also considered gentiles) suffices to get married with designation as stated Rambam chapter 9 of Hilchos Melachim.

In Rambam Hilchot Melachim 9,8:

וּמֵאֵימָתַי תִּהְיֶה אֵשֶׁת חֲבֵרוֹ כִּגְרוּשָׁה שֶׁלָּנוּ מִשֶּׁיּוֹצִיאֶנָּה מִבֵּיתוֹ וִישַׁלְּחֶנָּה לְעַצְמָהּ. אוֹ מִשֶּׁתֵּצֵא הִיא מִתַּחַת רְשׁוּתוֹ וַתֵּלֶךְ לָהּ. שֶׁאֵין לָהֶם גֵּרוּשִׁין בִּכְתָב. וְאֵין הַדָּבָר תָּלוּיִ בּוֹ לְבַד. אֶלָּא כָּל זְמַן שֶׁיִּרְצֶה הוּא אוֹ הִיא לִפְרשׁ זֶה מִזֶּה פּוֹרְשִׁין

When would a married woman be (i.e gentile) be considered divorced? When her husband expels her from his house or if she leaves herself, for there is no written divorce, and it's not up to him alone, but whenever he or she wants to leave each other, they are divorced.

Abraham our Patriach before Mattan Torah was Married to Sarah through consummation in his domain(Genesis 20,3) in the Same manner as Gentiles as stated in Yerushalmi Kiddushin 1,1:

בנכרים רבי אבהו בשם ר' אלעזר כתיב (בראשית כ׳:ג׳) הנך מת על האשה אשר לקחת והיא בעולת בעל על הבעולות הן חייבין ואינן חייבין על הארוסות מילתיה דרבי אלעזר אמרה והוא שנתכוון לקנותה

What is marriage for gentiles? Rabbi Elaazar said Its written regarding Avimelech King of the Philistines (Bereshis 20,3): "You will die because of the woman (Sarah) you have seized, yet she is consummated to a Husband (i.e Abraham)" -on consummated wives one is liable to death but not for betrothed wives, and even regarding consummated wives one needs intent on marriage (i.e not prostitution).